.357 magnum is plenty for dear, and can even work on black bear if you chose the right load (preferably 180 or 200 grain bullet).
There is the following effective loads:
Georgia Arms Deerstopper (158 grains @1450 fps)
Cor Bon 180 grain @ 1285 fps (from a 4" barrel)
Cor Bon 200 grain penetrator @ 1200 fps (from a 4" barrel)
I wouldn't shoot these hot loads in guns other than a Freedom Arms revolver, Ruger Blackhawk, Ruger Bisley, Ruger Redhawk (.357 version), or GP 100. The S&W 686 might be able to handle it as well, but I think the Rugers and Freedom Arms are more suited for the hotter loads mentioned above.
The great thing about a .357 is that you can load down to .38 special for practice, and .38's are super cheap in my area. .44 Special loadss, OTOH, tend to be nearly as expensive as .44 magnums! If you get a .357, get AT LEAST a 6" barrel. You will need good shot placement, since you are giving up some power to the bigger cartridges. The longer sight radius will get you better shot placement (if you do your part), and the longer barrel increases your bullet's velocity.
A good compromise round is the .41 magnum. It offers enough power to take most North American critters down, but doens't recoil as fiercly as a heavy .44 magnum load. The disadvantage of the .41 maggie is high price, and low availability.